Yes, but please be reminded that this is a color scheme for alternate history.You mean that video here:?
It's pretty funny. And yeah, the emperor and the shogun are technically two separate power bases. But in practice, during the entire shogunate period, the emperor was essentially a figurehead with no real power. Add to that the fact that modern Japan claims to be the legal successor to both, and the period in which the two existed as separate independent autonomous countries is limited (on a par with the few months in which the Ottoman Empire and the Republic of Turkey existed simultaneously), and there's fairly solid grounds for living it as is.
As for Britain, there was a certain civil war lasting a few years which featured monarchist and republican factions. And my "Commonwealth" colour is intended to specifically cover situations that either exclude the British Isles (e.g., Angrezi Raj) or act as an umbrella multinational colour NOT dominated by the UK (no OTL examples). Mercia had a substantial history as an independent country lasting a few centuries.
It could be quite possible that an empire versus a shogunate TL could pop up and they'll ask why there's no shogunate color like in TACOS.